Enhanced Sensitivity to Local Dynamics in Peptides by Use of Temperature‐Jump IR Spectroscopy and Isotope Labeling

Abstract Site‐specific isotopic labeling of molecules is a widely used approach in IR spectroscopy to resolve local contributions to vibrational modes. The induced frequency shift of the corresponding IR band depends on the substituted masses, as well as on hydrogen bonding and vibrational coupling. The impact of these different factors was analyzed with a designed three‐stranded β‐sheet peptide and by use of selected 13C isotope substitutions at multiple positions in the peptide backbone. Single‐strand labels give rise to isotopically shifted bands at different frequencies, depending on the specific sites; this demonstrates sensitivity to the local environment. Cross‐strand double‐ and triple‐labeled peptides exhibited two resolved bands that could be uniquely assigned to specific residues, the equilibrium IR spectra of which indicated only weak local‐mode coupling. Temperature‐jump IR laser spectroscopy was applied to monitor structural dynamics and revealed an impressive enhancement of the isotope sensitivity to both local positions and coupling between them, relative to that of equilibrium FTIR spectroscopy. Site‐specific relaxation rates were altered upon the introduction of additional cross‐strand isotopes. Likewise, the rates for the global β‐sheet dynamics were affected in a manner dependent on the distinct relaxation behavior of the labeled oscillator. This study reveals that isotope labels provide not only local structural probes, but rather sense the dynamic complexity of the molecular environment.


Introduction
Protein activity is intimately linked to local structure and dynamics, for example, by positioning functional groups or substrates in enzymes, therebya llowing the structure to execute biochemical processes.Ac omprehensive view of protein-folding mechanisms requires an understanding of dynamics and structure. [1] Determining how ap rotein achievess uch af unctional and stable, low-energy state is at the core of both the overall protein-folding problem and growing interesti nm isfolded proteins,w hichb ecome trapped in even lower energy minima. Many degenerative diseases have their pathology rooted in protein misfolding anda ggregation, whicho ften involves conformational transitions to b-sheet structures. [2] Thus, delineating the stabilizing interactions and factors that affect conformational dynamics of b-sheets is of particular interesti n biophysical research on protein folding, misfolding, and aggregation.D etermination of the protein backbones tructure, or fold, and its dynamics requires methods that sense the coupling of specific peptide units,w hich form the fundamental polymer chain and that are capable of ar elativelyf ast response upon structuralchanges.
Vibrational spectroscopy provides au seful means for attaining molecular-scale insights into structural and dynamic properties of proteins. IR spectra are particularly beneficial in analyzing b-sheet structures. [3] Global secondarys tructure changes can be monitored with equilibrium and dynamic techniques by probing the amide Ib and, which involves the C=Os tretching modes of the polypeptide backbone. By contrast, electronic circulard ichroism (ECD) in the UV region, l > 200 nm, is weak for sheet structures, [4] and fluorescencem ainly detects changes in tertiary structures.N onetheless, optical spectra are low resolution and lack site-specific sensitivity to local structural variations. However,b yt he use of isotopics ubstitution, contributionso fi ndividual modes can be resolved and identified in both equilibrium and dynamic vibrational spectroscopic studies. [5] In particular, the substitution of selected amide C=O groups with 13 Cl eads to IR amide If requencies downshifted by about 40 cm À1 from where they would appear in the spectrum if isolateda sa 12 C=Om ode. The properties of such isolated 13 C=Om odes can be attributed to local conformationsa nd their dynamic changes. [5,6] It should be noted that frequency shifts for single-labeledp eptides alone are not sufficient to determinel ocal structure, but their changes upon unfolding can be diagnostic, particularly if the stable structure is determined independently with other techniques. If two or more such labeled residues are incorporated into the sequence, their specific coupling can be exploited to betterd eterminel ocal structure;this is often aided by theoretical modeling. [7] Beyond structure, isotopic substitution provides am eans of studying site-specific, fast dynamics of b-sheets that can be accessed using laser-induced temperature-jump (T-jump) spectroscopyw ith tunable single-wavelength IR detection. [8] Herein, we used T-jump IR techniques to gain new insights into the spectroscopic and folding properties of isotopically labeled bsheet model peptides. Many studies have utilized sequence designsw ithc ross-strand aromatic interactions [9] and/or turn-promoting sequences [10] to initialize the formation of b-hairpin structures. Previously,w er eported spectra and dynamics for a series of three-stranded double hairpin designs [8g,i] based on the very stable D ProÀGly turn sequence. [8i, 10b, 11] However,i ts strong structuralc onstraintsc an overemphasize the role of turns in the folding mechanism. [12] Substituting the turns with AibÀGly( Aib = a-aminoisobutyric acid) sequences, following the designs of Hammer and co-workers, [7b, 13] can relieve some of these conformational constraints and eliminate spectral overlap of 13 C=O-labeled peptidem odes with those of the XxxÀPro peptidel ink, while still promoting turn formation in aqueous solution.T he sequences we study herein form threestranded sheets, the central strands of whicha re hydrogen bondedt ob oth the first and third strands;t his mimics interactions in am ore extended sheet structure. We additionally incorporated aT rpÀTyrc ross-strand interaction between the first two strands to preferentially stabilize that hairpin, following previouss tudies. [8i, 9a] We analyzed the impact of various labeling schemes on IR spectra and, in particular, on T-jump-induced relaxation rates. Resultsw ere compared with complementaryq uantum mechanical spectral calculations, NMR structures, and molecular dynamics (MD) simulations. Unexpectedly, we observed only minor effectso fc ross-strand coupling for labeled residues in the equilibrium IR spectra,w hereas the siteselected T-jump-induced kinetics obtained with isotope-labeled probes had significantly enhanced sensitivity to coupling.

Experimental Section
The sequence of the peptides used in this study (SVKLWTS-BG-KTYLEV-BG-TKVLQE-NH 2 ;B= Aib [13] )w as modeled after ad esign of Gellman, [14] as discussed previously, [8i] and is illustrated in Scheme 1. Substitution of AibÀGly for the D ProÀGly turn sequence used by Gellman was suggested by our earlier demonstration that the AibÀGly sequence supported hairpin formation. [11c, 13, 15] Isotopic labels, 13 Co nt he amide C=O, were introduced at specific positions roughly centered on the three b-strands of the peptide (at Leu4, Leu13, and Val20). These substitutions were chosen to enable cross-strand multiple labeling that could potentially increase the intensities of the shifted bands. It is clear from the R À3 dependence of dipole coupling that placing labels close within the sequence leads to stronger coupling, but for opposing strands this can be more complex. We previously found that forming small crossstrand hydrogen-bonded rings in hairpin structures led to significant coupling and herein incorporated that into our design. [8d, 13, 16] Label placement provided at est for coupling across strands 1-2, for labels on residues Leu4-Leu13;a cross strand 2-3, for labels on Leu13-Val20;a nd, as ac omparison, labeled on all three strands. The peptides were named according to the label positions. Consequently,t he single-label variants were 1W-4, 1W-13,a nd 1W-20; the double-labeled variants were 1W-4-13 and 1W-13-20,a nd the corresponding triple-labeled variant was 1W-4-13-20.A dditional residues, including Gly9, Val15, Gly17, and Leu21, were labeled and investigated using FTIR spectroscopy for further testing of the computed model force field (FF).

Peptidesample preparation and FTIR spectroscopy
Peptides were obtained from SciLight Biotechnology LLC, Beijing, P. R. China, after being synthesized by using standard fluorenylmethoxycarbonyl (FMOC) methods. Sample purity in each case was judged as > 95 %b ased on MS and HPLC analyses. Sample preparation and temperature-dependent equilibrium IR spectra for all isotopically labeled variants were obtained, as described previously. [8i] Further experimental details are also given in the Supporting Information. Te mperature-dependent IR spectra were measured over the temperature range of 5-95 8Ci ns teps of DT = 5 8C, and the results were analyzed by using singlevalue decomposition (SVD) methods. The peptides were dissolved in D 2 Oa t 10 mg mL À1 at acidic pH and lyophilized threefold to remove trifluoroacetic acid (TFA) and effect H/D exchange before being placed in ah omemade demountable cell consisting of CaF 2 windows with aT eflon spacer (100 mmo ptical path length). Samples for T-jump experiments were prepared similarly.

T-jump relaxation dynamics
Relaxation kinetics were obtained by using the laser spectrometer we have described in detail separately. [8h, 12] In brief, ap ulsed Qswitched Ho:YAG laser (IPG Photonics Corporation, USA) operated at l = 2090 nm was used to excite as olvent (D 2 O) vibration, there-by rapidly increasing the sample temperature. To improve uniform sample heating, the pump beam was split into two counter-propagating beams, both focused on the sample, with one delayed, leading to an effective pulse duration of~15 ns. The rapid T-jump perturbs the folding equilibrium on at imescale faster than that of the molecular dynamics of interest. Ac hopper was synchronized with the 10 Hz pump laser and blocked each second pulse to provide ar eference signal with no excitation, which resulted in an excitation repetition rate of 5Hz. The pump energy was set to amaximum of 14 mJ to yield aT -jump magnitude of~8 8C; however,f or experiments at the lowest final temperatures of~5 8C, as maller jump was required and obtained by reducing the pump power with neutral density attenuators. Relaxation dynamics of the peptide were probed at selected wavenumbers with aq uantum cascade laser (QCL), installed in aM IRcat-QT laser system (Daylight Solutions Inc.,U SA). The continuous-wave (cw) QCL used (M2062-PCX) had at uning range from 1730 to 1480 cm À1 ,w hich was ideally suited for the 13 C=Oi sotope studies. The probe laser beam was focused on the sample within as pot (Ø~300 mm) that was significantly smaller than that of the excitation beams (Ø~2mm), to assure measurement of ahomogenously heated volume. To correct for the influence of solvent kinetics, the sequentially measured solvent-only signal was scaled and subtracted from the peptide sample signal to result in af lat baseline after completion of peptide relaxation. The final temperature after the T-jump was determined from the change in absorbance of the solvent, which was measured under the same pumping conditions, and by calibration with temperature-dependent FTIR spectra of D 2 Oa sareference. [8g] Relaxation kinetics for~1000 transients were averaged and evaluated for the time interval from 300 ns up to 1.2 ms by using am onoexponential decay function. Time constants, t,w ere determined for different final temperatures, varying from 5t o 50 8C, and the resultant rate constants, k,w ere fit to an Arrhenius relationship.

Structures determined by NMR spectroscopy
An ensemble of best-fit low-energy structures was determined for ac losely related peptide (SVKIWTS-BG-KTYTEV-BG-TKTLQE-NH 2 )b y analysis of 2D NOESY,T OCSY, and COSY NMR spectra. The use of structural data for this alternate sequence was supported by higher solubility,v ery similar chemical shifts in both sequences for the conserved residues, and the fact that the circular dichroism (CD) and IR spectra, as well as T-jump kinetics of this alternate sequence and that used for the T-jump studies, were almost identical. Structures were obtained for the peptide at 283 Ki n9 0:10 H 2 O/D 2 O, at~6mgmL À1 concentration (~2-3 mm), by using an 800 MHz instrument with the same methods as those detailed previously. [8i, 12] Spectra were processed within NMRPipe, [17] viewed/assigned in NMRView, [18] and NOESY signals were manually selected and assigned with CYANA 2.0. [19] Data regarding NMR results and structure determination are available in Ta ble S1 in the Supporting Information. The 10 lowest energy unique structures were refined by restrained MD within AMBER8, [20] by using the ff99sb FF, [21] and were used to guide our subsequent spectral simulations and analyses.

Molecular dynamics
Simulations were carried out on the lowest energy NMR spectroscopy structure, which was obtained as described above. Briefly,t he peptide was solvated in ab ox of TIP3P water,e nergy minimized, and annealed in am ultistep process, as detailed previously. [12] Unrestrained 200 ns NPT MD trajectories were carried out at 300 Kb y using the Amber FF FF14SB. CPPTRAJ [22] was used to analyze the trajectories for information such as variation of torsional angles in turn residues and interatomic distances between strands for selected hydrogen bonds.

Spectralcomputations
To provide some measure of spectral sensitivity to structure variations, spectral simulations for as et of 23-residue all-Ala peptides, each constrained to selected conformations, as determined by NMR spectroscopy (see above), were carried out at the DFT level (BPW91/6-31G**/PCM) using Gaussian 16. [23] The methods used closely followed our previous study, [12] and are detailed in the Supporting Information. To account for the differences in central and outer-strand hydration effects, DFT force fields (FF) were empirically adjusted to better reflect experimental frequency shifts of single-labeled variants.

Structural aspects
The introduction of 13 C=Ob ackbone isotope labels into bsheet structures maximizes the potential for structural analysis by IR spectroscopy,i ft hey are strongly coupled. Ideally, one mights eek to design ap eptidet hat forms three antiparallel strandsfully hydrogen bondedtoeach other and interconnected by tight turns, which result in only am oderate twist of the overall structure. DFT simulations of af ully minimized, unrestrained three-stranded structure show significant intensity and frequency changes for double-labeled peptides that are indicative of strong couplingb etween strands. For the strongest coupling cases, the amide I' (I' indicates H-D exchanged) modes, corresponding to the single labels, were at similar frequencies. The predicted IR spectra for labeled variants of such an ear-ideals tructure are illustrated in Figure S2 in the Supporting Information.
This design goal was approached in our previous study of the pG2 peptide, but the D ProÀGly turn sequence, in thatc ase, led to spectral interferences that inhibited interpretation of the impact of isotopic labeling on strand dynamics. [12] To avoid this interference, we converted relateds equences [8i] to incorporate AibÀGly( BG) turns, which also support hairpin formation in water,a sp reviously demonstrated with two-strand models. [7b, 11c, 13] Our initially prepared AibÀGly variant incorporated an aromatic cross-strand contact in the first, strand 1-2, hairpin (SVKIWTS-BG-KTYTEV-BG-TKTLQE-NH 2 )a nd resulted in as table three-strand sheet structure, as confirmed by NMR structure determination, as well as IR and CD spectra.T his sequence was subsequently mutated, I4!L4, T13!L13, and T20!V20, to yield SVKLWTS-BG-KTYLEV-BG-TKVLQE-NH 2 ,w hich allowed easier isotopicl abeling with only minor effects on the structure. The similarityo ft heir folds was shown by IR and CD results, as well as T-jump kinetics, which were virtually the same for both sequences, although the revised sequence was somewhat more stable (based on temperature-dependent IR).
The NMR-determined structures show that this modified peptidei sq uite twisted, and overlapping the ensemble of the best-fit structures suggests that the terminia re disordered ( Figure 1). The first turns (Aib8-Gly9) are quite uniform for the 10 best-fit structures, but the second turns (Aib16-Gly17) vary more or less continuously between two extrema.T urn 2d oes maintain f,y torsions representative of type 1' turns (see Ta ble S3 in the Supporting Information), unlike the two-state structures found for the D ProÀGly turns in our previous papers. [8i, 12] The apparent variations in turn 2a re thusn ot local, but are aconsequence of small deviations from the mean positions in their neighboring residues.
The 300 KM Da nalysesi ndicate somewhat different structural variations, but also support the relative stability of the turns, which have only short-lived deviations away from type 1'.S imilarly,t he inner parts of the three-stranded structure, in which the 13 C=Ol abels are placed, remain folded in the MD simulations, whereas the termini are highly dynamic, as observed from differences in average hydrogen-bond distances (Table S4 in the Supporting Information). The NMR data imply that the C terminus has somewhat more disorder than that of the Nt erminus and that the hairpin betweens trands1 and2is more complete and uniform, on average. This appears to be ad irect consequence of the cross-strand stabilization inducedb yt he aromaticT rpÀTyri nteraction (of residues 5a nd 12), which is very stable in both NMR and MD results. In contrast to the edge-to-face TrpÀTyrg eometry observed for the tryptophan zipper (Trpzip) variants, [9a,b, 16, 24] the aromatic interaction in this peptidei sm ore of an offset stacking arrangement, similart o our previous D ProÀGly turn-based studies. [8i] Clearly,i nt he actual structure, the N-and C-terminal strandsa re not equivalent because both are distorted by disorder;b ut the hairpin formed with strands 1-2 is quite regular aside from the N-terminal residues,a se vident from the overlaids tructures in Figure 1. Thus, one anticipates coupling between residues in these strands. The other hairpin between strands2 and 3i s less well formed and the consequences for coupling are more difficultt op redict. Finally,t he computed MD trajectories also show largem otions for the terminal residues that suggest use of as ingle structure for spectral simulation is likely to be in-complete at best, which has led us to comparespectral simulations for selected structures derived from the NMR spectroscopy best-fits et.

Shifting IR frequencies by isotopic labeling
The low-temperature IR spectra of all peptidev ariants ( Figure 2) exhibited characteristics of antiparallel b-sheets. For the unlabeled variant, 1W,t his is indicated by am ajor band at 1634 cm À1 ,w ith aw eaker shouldera t~1674 cm À1 .
Upon heating, the IR bands broaden and shift their maxima to 1648-1652cm À1 ,w hich indicates thef ormation of ad isordered state ( Figure S5 in the Supporting Information). The very gradualt ransition indicated al ow level of cooperativity with an apparent T m of~73 8C, which was determined by fitting the derivativeo ft he SVD second component versust emperature plot for the amide I' band shape( Figure S6 in the Supporting Information). [25] As expected, the introduction of isotopicl abels gave rise to additional bands at lower wavenumbers ( Figure 2a  (Some additional isotopically labeled variants were prepared, for which resultsa re given in FigureS7i nt he Supporting Information.) In contrasttoe xpectations for an ideal structure, in which local amide frequencies in each strand are the same, the frequencies of these bands show as trong dependency on the location of the oscillator within the b-sheet. If the centrals trand (Leu13)i sl abeled, a shoulder at 1607 cm À1 is observed, but if the peptideislabeled on outer strands, lower wavenumberb ands arise. Furthermore, the orientationo ft he labeled group has an impact. Val20, with its 13 C=Op ointingi nt owardt he central strand, leads to a band at 1588 cm À1 ,w hereas Leu4, with 13 C=Op ointing out toward the solvent, has ah igherw avenumber band at 1594 cm À1 .( By comparison, Gly9 andG ly17 also point out and, if labeled, have bandsa t1 591 cm À1 and 1592 cm À1 ,s ee Figure S7 in the Supporting Information;t his suggests am easurable differenceb etweeni nternal hydrogen bondingt oa mides and solvation by water.) This lack of degeneracy for the various isotope positionsr educes the impact of their mutual crossstrand coupling. Labeled Val20 (andp ossibly also Leu4) gives rise to an additional minor side band at~1610 cm À1 ,w hichi s most evident in the difference spectra (Figure 2). The side band relatedt oV al20i sr eproducible, which is consistent between peptides with different labeling patterns and is not attributable to impurities, as shown by the MS and HPLCr esults, as well as its appearingi nt he spectra of each of the labeled samples containing Val20. We do not have ac onclusive assignment of this observed feature. However,wec an suggest that it arises from conformational equilibria thate ncompass more structuralv ariation in the C-terminal residues than in the N-terminal ones, which will affect Val20 more than Leu4.  1588 cm À1 ,w hichc an be attributed to the labeled Leu13 in both and Leu4 or Val20i ne ach, respectively.T his behavior is different from that observed in our previous studies of hairpins with cross-strand labels. Thosep eptides had more strongly coupled transitions, for which the two isotope-shifted modes generatedo verlapping bands with quite different intensities, the individual contributions of which could not be distinguished. [7b, 8d, 13] The nondegeneracy seen hereo bscures coupling, and the roughly equivalent intensity in both bands implies that it is weak. However,t he labeled oscillators are coupled, to some extent, as witnessed by shifts of the double-label bands in 1W-4-13 up and down in frequencyf rom that found in 1W-4 and 1W-13,r espectively,c an be observedf rom the values in Ta ble 1. The shift of Leu13 (~3cm À1 )i sl ess than that for Leu4 (~7cm À1 )i n1W-4-13,w hich is asymmetric, but substantial. By contrast, it is much less (~1cm À1 )f or Leu13 and Val20 in 1W-13-20,w hichs uggestsadifferencei nc oupling for stands1 -2 and 2-3, the latter being much weaker.T he spectrum of the triple-labeled variant 1W-4-13-20 appears to be ac ombination of the respective single-and double-labeled sequences, resultingi nastronger intensity for the band at~1588 cm À1 due to contributionsf rom both labels in the outer strands. By contrast,t he higher frequency band, associated with Leu13, has an intensity in 1W-4-13-20 similar to that in both doublelabeled variants and in 1W-13,a ll of which have one label in the central strand.T hus, both labeled positions in 1W-4-13-20 have equilibrium IR intensity patterns that reflect virtually independent spectral contributions to the overall band. Another impact of the introductiono fm ultiple labels is as hift of the main b-sheet band to higherw avenumbers (Table 1), which is largestf or the triple-labeled variant (up to 1642 cm À1 ). Disruption of the vibrational couplingi nt he b-strands by isotopic substitution effectively shortenst he coupled segments in the strand and results in less excitonic splitting. [7a,b,d] Thus, the higher intensity,l ower frequency b-strand component (1634 cm À1 in 1W)i ss hiftedt oahigherw avenumberi nt he labeled variants due to disrupted coupling. For variants labeled in strand 1, this shift is~2-3 cm À1 more than that for those labeled in strand 3, which indicated removal of Leu4 has as tronger impact on b-sheet coupling than that of Val20, and thus, reflects the higherdegree of order in strand 1.

Computed IR spectra
The isotope-labeled three-stranded structure does not showI R frequency shifts, as expected, from an ideal structure( Figure S2 in the SupportingI nformation), so we computeds pectra for several structures determined by meanso fN MR (a representative one of which is shown in Figure S8 in the Supporting Information). In an ideal structure, coupling would result in splitting of the mode frequencies equallyu pa nd down from the mean of the single-label positions and, for this geometry,t he lower component would have mosto ft he intensity.H owever,  our experimental resultsf or the double-labeled variants show only smaller,a symmetric frequency shifts and reflect as imple summing of the single-label resultst hat indicate minimal coupling and suggest ideal simulations would be inadequate for explaining the observed spectra. Spectra were simulated by using peptidesc onstructed with only Ala residues (except for two pairs of AibÀGly turn residues), the torsions of whichw ere constrained to values that corresponded to selected examples taken from the ensemble of best-fit NMR-determined structures. Spectral computations at only the BPW91/6-31G** level, for the lowest energy NMR-derived structure,g ave the wrong relative frequency ordering for the labeled L4, L13, and V20 bands. Incorporating an implicit solventc orrection with ap olarizable continuum model (PCM) provided improvement, but addition of an empirical selective scalingo ft he FF for those C=Og roups that pointed out to the solventw as required to obtain qualitativelyi mproved relative frequencies. [12] This correction empirically adjusts the single-label frequencies to account for hydrogen bonding to water.I ft his were done quantum mechanically for explicit solvent, it would require both a very large calculation and unrealistically frozen or restricted water conformations.E ven after correction, these calculations should be viewed as quite approximate, in that solventa nd side-chain effects are only empirically accommodated.
To test for sensitivity to conformational variation, we performed similar calculations for three differents tructures from the 10 best fits to the NMR-determinedc onstraints. The absolute frequencies for single-labeled residues varied, but the relative frequency variation remained, with amide Im odes of positions 4a nd 20 being too high, with respectt ot hat for position 13, even when using PCM corrections (data not shown). Only after alteration of the FF to account for the differencei ns olvation of edge versus central strands( Figure S8 in the Supporting Information) could we compute the qualitativelycorrect ordering for positions 4a nd 13, compared with the experimentally observed frequencies (Table 1). For position 20, the frequencyr emained too high. By using these corrections, the mode character of the molecule, if double-or triple-labeled, could be probed. The coupling constantsf or the labeled residue on the centrals trand (13) to the other strandsa re nonzero, buts mall, and coupling to the neighboring residues in the strand is just slightly stronger.T he calculations do not show as tronger coupling for 4-13 relative to that of 13-20 ( Figure S8 in the SupportingI nformation), in contrast to the experimental pattern.

Site-selective T-jump dynamics
Isotopel abels can be used to visualize the dynamics and interactions of individual oscillators, while not alteringt he folding mechanism of the peptide. Figure 3r epresentatively shows, for the triple-labeled peptide 1W-4-13-20,h ow site-specific relaxation can be monitored by time variation of the entire amide I' spectruma fter aT -jump. The disordered, b-sheet, and isotopeshifted bands give rise to four,r esolved, dynamically detectable changes. Consistent with the equilibrium results above (Table 1), the changes in the 13 C=Ob and associated with Leu13 (1608 cm À1 )a re clearly distinguished from those for Leu4 or Val20, which are spectrally unresolved (1588 cm À1 ), but have different, resolvable kinetic relaxations (see below). The change of absorbance after the T-jump was remarkably strong for the labeled modes,i np articular,f or the Leu13b and at 1608 cm À1 .G iven the trends in Figure 3, it is sufficient to follow dynamics at only the peak frequencies to access their separate behaviors (see an example of single-wavenumber transientsinF igure S9 in the Supporting Information).
Relaxation dynamics of different parts of the peptide were determined at selected wavenumbers and for final temperatures over the range of~5-50 8Ci nt he amide I' region based on their response in the difference spectra ( Figure S5 in the Supporting Information). The loss of b-sheet structure was monitored at~1629 cm À1 (Figure S10 a,b in the Supporting Information). Additionally,t he rise of disordered structure was probeda t~1662 cm À1 ( Figure S11a,b in the Supporting Information). The loss in intensity for the two 13 C=Ob ands was probeda t~1588 (Figure S12a in the Supporting Information) and 1608 cm À1 (S12 bi nt he Supporting Information), respectively.
After correction for solventc ontributions, the relaxation transients of the peptidew ere fit to am onoexponential function to derive rates. The observed time constants are less than 5 msa t1 0 8Ca nd~1 msa t5 0 8C; these values are slightly slowert han those for the relatedp Gv ariants. [8i] Ar epresentative selection of relaxation times at 10 8Ci sg iven in Table 2. Unlike for at wo-state folding process, which should have uniform relaxation rates, the variationo bserved in Ta ble 2f or selected wavenumbers indicates that different local dynamics are sampled, both in the shifted isotope bands and in the b-sheet bands. These rate divergences are more evidenta tl ow temperatures, as shown in Figures S10-S12 in the Supporting Information.
Considering the frequency-shifted isotope modes (~1588 and~1608cm À1 ), the slowest relaxation time (t = 2.74 ms) is observed for the outer-strand labeled carbonyl on 1W-4.T he  13 C=Ob and in the first strand is presumably due to stabilization of the first hairpin by the crossstrand aromatic interaction. [8g,i] The labeled band for 1W-13, mostly describing the central strand, has af aster relaxation than that in 1W-4.T he relaxation of the C-terminal outerstrand label for 1W-20 is faster than that for 1W-4 and similar to that for 1W-13.I fa ttention is shiftedt ot he overall b-strand dynamics, measured at~1629cm À1 ,t he opposite trends occur, in that 1W-13 has by far the slowest b-strand change (t = 3.46 ms) and 1W-4 and 1W-20 are faster.D ifferences in relaxation time constants are small;h owever,t rends are consistent not just for the 10 8Cd ata shown in Ta ble 2, but also over a wide temperature range, as observed from the Arrhenius profiles illustratedi nF igure 4. Although the isotope bands of 1W-4 and 1W-20 both occur at~1588 cm À1 ,t heir best-fit relaxation times differ for the entire temperature range,o ver which the band in 1W-4 hass lower dynamics than that in 1W-20 ( Figure 4a). So, the less-structured thirds trand has faster dynamics than the more ordered first strand,w hich fits expectations from the NMR-determined structural disorder.

Impact of labeling schemes on rate constants
Our study clearly demonstrates that the observed rate constants probeda taselected wavenumber change depending on the labeling scheme. In the double-labeled variants (Table 2), the pattern of Leu4 being slower than Val20 is reflected in the 13 C=Ob and relaxation at~1588cm À1 for 1W-4-13 (t = 1.67 ms) being slower than that for 1W-13-20 (t = 1.30 ms). Additionally,t he incorporation of labels on different strandso f the peptidei mpacts the relaxation kinetics for both sites, as indicateds chematically in Figure 5. Substituting 13 C=Ot oL eu13 decreases the time constantsf or both Leu4 and Val20. Inversely,t he addition of 13 C=Oo ne ither Leu4 or Val20 increases the time constants for Leu13. These experimentally observed changes reflect coupling and are represented in at emperature-dependent manner in Figure 6, although cross-strand interaction is less pronounced than it would be found for an ideal structure. Even weak coupling is revealed by ac hange in the time constantb ecause added isotope substitutionsc ontribute to the probed amide-modef requency.T hus, if an amide oscillator of another part of the peptide is isotopically labeled and couples to the probedo scillator,t he resultingt ime constant will change accordingly,that is, if the coupling oscillator has ah igherf olding rate, the observed rate (k obs )g ets higher and vice versa. [a] Values were obtained by fittingt he temperature-dependent kinetic data to the Arrheniusr elationshipt of acilitate ac omparison of relaxationt imes at one specific temperature for each band and variant;the error was determined by the regular residual as the mean of individual measurements over atemperature range of (10 AE 3) 8C. Figure 4. Relative relaxation behavioroft he single-labeled variants shownas Arrheniusp lots. a) 13 C=Omodesp robed at~1588cm À1 for 1W-4 (green squares) and 1W-20 (blue circles) and~1608 cm À1 for 1W-13 (red triangles), and b) b-sheetcontributionprobed at~1629 cm À1 ,including 1W (black diamonds). The lines represent fits to the Arrheniusequation to provideaqualitatived escription of the temperatured ependence.
The triple-labeled variant, 1W-4-13-20,c ontainingc ontributions of both terminal strands has relaxations that partly reflect the dynamic behavior of the double-labeled variants.A t 1588 cm À1 ,r elaxation is similar to that of 1W-4-13,a nd faster than those for 1W-4 and 1W-20,w hereas at 1608 cm À1 the re-laxationi sm ore like that of 1W-13-20,w hich is again slower than that for 1W-13 (Table 2a nd Figure 6). This might indicate that relaxation probeda t1 588 cm À1 is dominated by strands1-2, whereas relaxation probeda t1 608 cm À1 reflects the coupling of strands2-3. In summary,f or both double-and triple-label cases, the impact of coupling on the kinetics of differently labeled residues was detected with highers ensitivity than that possible by using equilibrium IR spectra.

Alteration of kinetics by removal of distinct residue contributions
Bands associated with the unlabeled 12 C=Or esidues,t hat is, the b-sheet band at~1629 cm À1 and the disordered structure at~1663 cm À1 ,a re affected when selected oscillators are shifted out of the main 12 C=Ob and to lower frequencies by isotopic labeling. For example, removing the relatively slow dynamic contribution of Leu4 from the 12 C-b-sheet band in 1W-4 (Figure S10 in the Supporting Information) leads to faster relaxation at 1629 cm À1 (2.03 msi nc omparison to 2.52 msf or the unlabeled peptide, at 10 8C). By contrast, removing Leu13 (which showst he fastestrelaxation) on the centrals trand in 1W-13 results in as ignificantly slower b-sheet relaxation (3.46 ms, Ta ble 2).
To some extent,t he same pattern can be seen in the disordered band dynamics. For example, Val20 in 1W-20 has af ast relaxation, yet relaxation for the disordered band at 1663 cm À1 in that variant is much slower than that for 1W. This, in particular, appliest ot he frayed ends of the peptide. Dynamicsf or 1W-21,w ith the label one residuec loser to the C-terminal end, were also measured as ac ontrol, and yielded much slower kinetics for its labeled oscillator than that found for 1W-20 ( Figure S13 in the Supporting Information). Correspondingly,t he kinetics fort he disordered structure in 1W-21 are faster than those for 1W or 1W-20,w hereas no significant difference was observed for its b-sheet kinetics.
In the presence of multiple labels, several opposing effects originating from the individual label positions have to be considered. In general, the impact on relaxation rates of removing ar esiduef rom as heet structure by isotopicl abeling is roughly additive, whichm eans that removing af ast relaxingr esidue slows the rate for what remains unlabeled.T he opposite Figure 5. Impact of additionallabelsont he relaxation time constants measured for the labeled oscillators at~1588 and 1608 cm À1 .T he relaxation time constants for the single-labeledr esidues (indicatedbyd ashed boxes)are altered by interaction with an additional 13 C=O. For the double-labeled variants (indicated by solid boxes), smaller time constants are observed upon detection at~1588 cm À1 (black, Leu4 and Val20, respectively), whereas the opposite effect occurs at~1608 cm À1 (gray,Leu13). change occurs, that is, increasing the rate for the unlabeled component, if as low relaxingr esidue is removed. This applies to relaxation times observed at both~1629 and 1663 cm À1 ,f or the b-strand and disordered components, respectively.

Local dynamics, stabilities, and relaxation rates
We have made as eries of isotopically labeled three-stranded hairpins and showed measurably different dynamics for selected positions within the strands. It seemsc lear from these variable rates that this model b-sheet peptidei samultistate folder. Investigation of the structure and spectralc onsequences can provides omei nsight into the local dynamics, as our datah as exposed.
With regard to the single-labeled variants,s ubstitution on the Leu4 residue (1W-4)y ields the slowest relaxation rates. Recalling that the equilibrium thermalt ransition has a T m of 73 8C, at this point k f = k u ,i fw er estrict the description to a simple two-state analogy for the overall folding and unfolding rate constants. All of our data sample relaxation after heating, but well below the equilibrium transition, that is, we operate under conditions in which the folded fraction, f f ,i sg reater than that of the unfolded fraction, f u .C onsequently, because k f /k u~ff /f u > 1f or T < T m , k f > k u and the observed relaxation rate constant, k obs~kf + k u ,m ust be dominated by k f .T he stability of the first strand or first hairpin is enhanced by the TrpÀ Tyrc ross-stranded aromatic contact, which, as we have previously shown, leads to slower contributions to the globalr elaxation kinetics. [8g,i] Here, we see that slower k obs is characteristic of the local dynamics of Leu4 as well, and presumably would mean k f is slower.B yc ontrast, the k obs values for Leu13a nd Val20 are similar.T hese two residues are hydrogen bonded in a small ring, which is characteristic of the antiparallel b-sheet structure. [7b,c, 13] Since we detect dynamics by ac hange in absorbance at as elected wavenumber,a st he strandss eparate in the unfolding/folding process, the absorbance for both will change, leading to their similar relaxation rates.
For double-labeled samples, we can detect and monitort he dynamics of each labeled residue separately,i nc ontrast to our initial expectations. Consequently,t he effects of coupling on the IR spectrum,i ntensitya nd frequency distribution, are reduced in such nondegenerate oscillator systems. However,t he labeled residues impact each otheri ni nteresting ways that are enhanced in the dynamics. Monitoring the Leu13 dynamics (1608 cm À1 ,F igure6b) under the influence of an additional label on Leu4 or Val20, we see ad ecisive slowing of relaxation for 1W-4-13 and 1W-13-20,r espectively.I fw ec onsider Leu13 to be in the most regularly folded part of the peptide, then k f for it should be fastest, that is,m ost favored to form. Adding Leu4 to this in 1W-4-13 can only slow k f ,since Leu4 is in aless folded segment,b ut this impact on the Leu13 band must be due to coupling to Leu4. If we regard the third strand as even more disordered, as observed in our MD and NMR results, then the additional slowing of k f for Leu13 in 1W-13-20 can be understood.A lternatively,i fw ec onsiderr elaxation at 1588 cm À1 , that is, for the labeled Leu4 or Val20b ands,a nd add Leu13, as is the case in 1W-4-13 or 1W-13-20,r espectively,t hen we are addingamore structured part of the molecule to the detectable relaxation process, and thus, k f increases through coupling again,a so bserved. These trendsa re all observed in Ta ble 2f or relaxation kinetics at 10 8C, but are also apparent in the global trendso ver the range of 5-50 8C, as shown in Figures4and 6. Viewing the data in the Arrhenius-style format, of log k obs versus1 / T,h elps to visualize these comparisons ab it more easily than that in terms of relaxationt ime constants versus T, but the relative differences are also evident in these alternatestyle plots(Figures S10-12i nt he Supporting Information).

Conclusion
Spectrale ffects of isotopicl abeling are highly sensitive to molecular structure and dynamics. If multiple vibrationally coupled sites are labeled, there is potential for am ore detailed structurali nterpretationo ft he data that derives from their through-space and through-bond couplings. Our study reveals that vibrational coupling is more sensitively probed by measuring site-selective kinetics than by analyseso fe quilibrium IR spectra.E veni ft he oscillators are not degenerate, resulting in conditions for which couplings can be difficult to determine from frequency shifts in the equilibrium spectra,d ynamic studies offer an ovel way to identifyw eak couplings. We observed that relaxation dynamics detected at single wavenumbers depended significantly on the contributing coupled oscillators. Differences in time constantsr eflect different couplings obtained withv arying labeling schemes.I ti si mportant to note that the folding mechanism of the peptidei sn ot affectedb y any isotopic substitutions, so that the incorporationo fmultiple 13 C=Ol abels can provide as ensitive, perturbation-free means of probing local conformationald ynamics. The enhancement in sensitivity to coupling observed herein in the analysiso ft he dynamics is an ew development and can open up the investigation of larger systems, in which single isotopic labels might be too dilute to generate measurable effects in equilibrium IR.